If, in the extensive calculus of the nth category, all the units (including i and the derived units E) are taken to be homologous instead of being distributed into species, we may regard it as a (2'-I)-tuple linear algebra, which, however, is not wholly associative.
This great muscle covers completely the supracoracoideus, generally described as the second pectoral, or subclavius muscle, in reality homologous with the mammalian supraspinatus muscle.
It is spheroidal, with the mouth and anus at opposite poles; there are five ambulacra, and the ambulacral plates are large, simple and alternating, each being pierced by two podial pores which lie in a small oval depression; the ambulacrals next the mouth form a closed ring of ten plates; the interambulacrals lie in single columns between the ambulacra, and are separated from the mouth-area by the proximal ambulacrals just mentioned, and sometimes by the second set of ambulacrals also; the ambulacra end in the five oculars or terminals, which meet in a ring around the anal area and have no podial pores, but one of them serves as a madreporite; within this ring is a star-shaped area filled with minute irregular plates, none of which can safely be selected as the homologues of the so-called basals or genitals of later forms; within the ring of ambulacrals around the mouth are five somewhat pointed plates, which Jaekel regards as teeth, but which can scarcely be homologous with the interradially placed teeth of later echinoids, since they are radial in position; small spines are present, especially around the podial pores.
The spore-bearing generation may throughout its phylogenetic history have been independent at one part of its life, and have been derived by modification of individuals homologous with those of the sexual generation, and not by the progressive sterilization of a structure the whole of which was originally devoted to asexual reproduction.
The development of the armature has been little studied, and the question whether there may be present gonapophyses homologous with those of the female is open.
The plates at the tips of the rays) in Asteroidea and Ophiuroidea, and therefore not homologous with the radially disposed plates often seen around the aboral pole of those animals.
Later still he engaged in the study of the relations between chemical constitution and rotation of the plane of polarization in a magnetic field, and enunciated a law expressing the variation of such rotation in bodies belonging to homologous series.
All organs performing the same function and showing similar adaptations are said to be analogous or homoplastic, whatever their morphological nature may be; hence organs are sometimes both homologous and analogous, sometimes only analogous.
The investigation also showed that the nature of the acid used affected the result, for in an homologous series of acids it was found that as the molecule of the acid became more complex, the rate of esterification became less.
The innumerable cases of structures, which are rudimentary and apparently useless, in species, the close allies of which possess well-developed and functionally important homologous structures, are readily intelligible on the theory of evolution, while it is hard to conceive their raison.